Solve for 2. Round to the nearest tenth, if necessary.
1 answer:
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Answer:
a) Sample mean: 48.71
Sample median: 48.3
Sample variance: 5.41
Sample standard deviation: 2.37
Step-by-step explanation:
a) Sample mean:
Sample median: M=48.3
Note: I order the data increasingly and take the value N / 2 = 40. In this way there are 39 values above and 39 values below the median.
Sample variance:
Sample standard deviation
b)
First, we have
(1 + 2/x²) (2x - 3/x)⁵ = (2x - 3/x)⁵ + 2/x² (2x - 3/x)⁵
In the expansion of (2x - 3/x)⁵, there is no x² term. Each term takes the form
where c is a binomial coefficient, and i is taken from the range {0, 1, 2, 3, 4, 5}. Looking at just the power of x in the product, we have
and 5 - 2i = 1 only if i = 2. By the binomial theorem, this term is given by
In the other expansion, we have an additional factor of 1/x², so that any given them in the expansion contains a power of x of the form
and 3 - 2i = 1 only if x = 1. This term in the expansion is
Then the coefficient of the x term in the whole expansion is 720 - 480 = 240.